Several prior studies have considered the role of directionality in population structure on the spread of mutant types [1]}, [2]}, [3]}, [4]}.
But in those studies the fitness advantage of the mutant is fixed, independent of type frequency. By contrast, our study considers frequency-dependent fitness effects that therefore describe game-theoretic interactions: an individual's payoff depends on both her type and her neighbors' types. The question of directionality in models of social behavior has been analyzed in at least one prior paper [5]}, but only in the case of two specific networks. Lieberman \(et. al\)  analyzed a directed circle network, where each node has one incoming neighbor and one outgoing neighbor, and a super-star network [5]}.
Whereas that work shows that directionality can influence the spread of cooperation, in those two specific cases the effect of directionality is to repress cooperation.
Our analysis applies to arbitrary network structures and we find that, in general, directionality tends to favor cooperation. Other studies have considered distinct networks of social interactions versus behavioral dispersal, limited to purely bi-directional links [7]}, [8]}.
